This is going to suck to read but it sucked more having to write. I just need to explain!

My first post! Most problems that I have I had been able to find on here. Thank you all for that!

I finally came up with one that I haven't found exactly what I have going on. I have been working on my wife’s 2002 trail Blazer 250 I’m not sure if the issues are related.
Fresh top-end (big bore) 74mm stock is 72mm. Do I need to re-jet? I’m at 2,000 to 2,400ft
I ordered a new cylinder and head that was bored and honed to match the piston now my old cylinder did not have an oil injection connection on the cylinder. It has oil injection but it hooks up to the carb so I put a vacuum plug over the oil injection port on the cylinder that is now installed on the bike. I don’t think this is an issue because I get nice blue smoke, and no over heat.

The first is the bike will only run at half choke. it will idle without choke and bog and die with any throttle is added. it will bog and die at full choke. I did a rush job crab clean (pulled jets and sprayed out carb passages and jets with carb cleaner then blew it out with the air compressor)set the air mix 1 turn out and tried to adjust it with no noticeable change same issue, so I ordered a rebuild kit, bought a can of carb dip and a new mounting boot (no noticeable cracks or leaks, but I’m getting desperate/frustrated.

The other issue is that the battery does not seem to be charging. We took it out for a ride for about three hours shut it off and restarted it a few times not till the last time when I was pulling it on the trailer it wouldn’t start with electric start, but started right up with the pull start. I rode around the block with the headlight on and the light didn’t get brighter with throttle or dim at idle.
I suppose the question is how do I test the stator and the voltage regulator? And when I took the carb apart it wasn’t glazed or clogged the float valve sealed could my idle/ bog issue be spark related? (Already replaced the spark plug

I take it you did a compression test and it's way up there? Just so we can dismiss a cracked ring/
If you're double sure the carb. and orifices are clean and in the boot all the way and air filter installed, it sounds as though you have a vacuum leak of some sort. Get the spray can carb. cleaner out and start squirting.
Could be crank seals.
As far as the charging system:
13-14.6 volts at 3000-4000 rpm's
5 amps or more at idle--most vlt-ohmeters do have an amp setting,disconnect neg. cable and hook volt meter from battery to cable, rope pull start ONLY.
If it fails the voltage output test,there's no neeed in doing the amp test.
Stator charge coil test:
yellow to yellow/red .22 ohms
yellow to ground infinity

Thank you for your reply. I haven't done a compression check because it has a new top-end. The ride was to try and get "things" to settle in. I did re check the head bolts, cylinder nuts, intake boot and exhaust flange and even made sure I didn't have a exhaust leak at the spring mounted pipe.
So with the crab spary will the motor rev up or start to die?

It should rev up higher as you are making it richer. Make sure the air filter is clean, they wont run with dirty filters at all those two strokers. Make sure your battery is good. If it isnt then the stator is basically running the bike but you wont have any reserve to restart it after you turn it off.

I think you need to pull apart your carb and do a thorough cleaning. My 500Ho did the same thing and it turned out that the needle get was warn and the c clip was all wobbly.

I dont think that is the same carb you have but you will have a needle jet.